(actually, my formula doubles the numbers you gave)

Are you sure? Suppose we take with , , then , so the values for should be as I gave them. And similarly for , giving values . Or else I have mis-understood your definition?

I’d simply see that as two separate partial preferences

Just to be clear, by “separate partial preference” you mean a separate preorder, on a set of objects which may or may not have some overlap with the objects we considered so far? Then somehow the work is just postponed to the point where we try to combine partial preferences?

EDIT (in reply to your edit): I guess e.g. keeping conditions 1,2,3 the same and instead minimising

where is proportion to the reciprocal of the strength of the preference? Of course there are lots of variants on this!

Sure, in the end we only really care about what comes top, as that’s the thing we choose. My feeling is that information on (relative) strengths of preferences is often available, and when it is available it seems to make sense to use it (e.g. allowing circumvention of Arrow’s theorem).

In particular, I worry that, when we only have ordinal preferences, the outcome of attempts to combine various preferences will depend heavily on how finely we divide up the world; by using information on strengths of preferences we can mitigate this.